Algebra Examples

${(\frac{- 6 a^{- 9} b^{5}}{2 a^{2} b^{- 4}})}^{4}$

Step 1

Move $a^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{- 6 b^{5}}{2 a^{2} b^{- 4} a^{9}})}^{4}$

Step 2

Multiply $a^{2}$ by $a^{9}$ by adding the exponents.

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Step 2.1

Move $a^{9}$ .

${(\frac{- 6 b^{5}}{2 (a^{9} a^{2}) b^{- 4}})}^{4}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{- 6 b^{5}}{2 a^{9 + 2} b^{- 4}})}^{4}$

Step 2.3

Add $9$ and $2$ .

${(\frac{- 6 b^{5}}{2 a^{11} b^{- 4}})}^{4}$

Step 3

Move $b^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{- 6 b^{5} b^{4}}{2 a^{11}})}^{4}$

Step 4

Multiply $b^{5}$ by $b^{4}$ by adding the exponents.

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Step 4.1

Move $b^{4}$ .

${(\frac{- 6 (b^{4} b^{5})}{2 a^{11}})}^{4}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{- 6 b^{4 + 5}}{2 a^{11}})}^{4}$

Step 4.3

Add $4$ and $5$ .

${(\frac{- 6 b^{9}}{2 a^{11}})}^{4}$

Step 5

Cancel the common factor of $- 6$ and $2$ .

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Step 5.1

Factor $2$ out of $- 6 b^{9}$ .

${(\frac{2 (- 3 b^{9})}{2 a^{11}})}^{4}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 a^{11}$ .

${(\frac{2 (- 3 b^{9})}{2 (a^{11})})}^{4}$

Step 5.2.2

Cancel the common factor.

${(\frac{2 (- 3 b^{9})}{2 a^{11}})}^{4}$

Step 5.2.3

Rewrite the expression.

${(\frac{- 3 b^{9}}{a^{11}})}^{4}$

Step 6

Move the negative in front of the fraction.

${(- \frac{3 b^{9}}{a^{11}})}^{4}$

Step 7

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 7.1

Apply the product rule to $- \frac{3 b^{9}}{a^{11}}$ .

${(- 1)}^{4} {(\frac{3 b^{9}}{a^{11}})}^{4}$

Step 7.2

Apply the product rule to $\frac{3 b^{9}}{a^{11}}$ .

${(- 1)}^{4} \frac{{(3 b^{9})}^{4}}{{(a^{11})}^{4}}$

Step 7.3

Apply the product rule to $3 b^{9}$ .

${(- 1)}^{4} \frac{3^{4} {(b^{9})}^{4}}{{(a^{11})}^{4}}$

Step 8

Simplify the expression.

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Step 8.1

Raise $- 1$ to the power of $4$ .

$1 \frac{3^{4} {(b^{9})}^{4}}{{(a^{11})}^{4}}$

Step 8.2

Multiply $\frac{3^{4} {(b^{9})}^{4}}{{(a^{11})}^{4}}$ by $1$ .

$\frac{3^{4} {(b^{9})}^{4}}{{(a^{11})}^{4}}$

Step 9

Simplify the numerator.

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Step 9.1

Raise $3$ to the power of $4$ .

$\frac{81 {(b^{9})}^{4}}{{(a^{11})}^{4}}$

Step 9.2

Multiply the exponents in ${(b^{9})}^{4}$ .

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Step 9.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{81 b^{9 \cdot 4}}{{(a^{11})}^{4}}$

Step 9.2.2

Multiply $9$ by $4$ .

$\frac{81 b^{36}}{{(a^{11})}^{4}}$

Step 10

Multiply the exponents in ${(a^{11})}^{4}$ .

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Step 10.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{81 b^{36}}{a^{11 \cdot 4}}$

Step 10.2

Multiply $11$ by $4$ .

$\frac{81 b^{36}}{a^{44}}$